Your analogy doesn't quite work because the difference between a high school swimmer and an Olympic swimmer is a difference of degree. That its, they both do the same thing, one is just (much) better.

But the difference between what people do when they take most math courses up to about their third year in college, and what mathematicians do, is a difference of kind, not degree. You can see my other comments in this thread to see what I think that difference in kind actually is.